Question

The common difference of the $A.P$. $b_1,b_2,.....b_m$ is $2$ more than the common difference of $A.P$. $a_1,a_2,.....a_n$. If $a_{40}=-159$, $a_{100}=-399$ and $b_{100}=a_{70}$, then $b_1$ is eqaul to

• A. $-127$
• B. $81$
• C. $127$
• D. $-81$

Answer 1

The correct option is D $-81$

$A.P$. $(a_1,a_2,a_3,.....a_n)$ $(C.D.=D_a)$
$(b_1,b_2,b_3,.....b_m)$ $(C.D.=D_b)$
$D_b=D_a+2$
$a_{40}=-159$
$a_1+39D_a=-159\cdots \left(i\right)$
$a_{100}=-399$
$a_1+99D_a=-399\cdots \left(ii\right)$
Equation $\left(i\right)-\left(ii\right)$
$-60D_a=240\Rightarrow D_a=-4$
$D_b=-4+2=-2$
$a_1+39(-4)=-159\Rightarrow a_1=-3$
$b_{100}=a_{70}$
$b_1+99D_b=a_1+69D_a$
$b_1+99(-2)=(-3)+69(-4)$
$b_1=-81$